Conserning the approximation of payments function by a set of normal distributions

The increase of stability is a strategic problem of any insurance organization. Alongside with others the stability of the insurance company is also defined by such a main factor as size of insurance payments. The optimized problem about the approximation of payments function, occupying the central place in mathematical models of actuarial mathematics by a set of normal distributions is considered. Statistical data on one of the insurance companies have been assembled in order to find the approached meaning of payments function. The functions of insurance payments in personal insurance have also been made. The given optimized problem has been solved due to the application of the package MATLAB 7.5.0. The offered technique is universal, and is applicable for various insurance companies. The received function $g(x)$ must be used for the numerical analysis of various characteristics of the insurance company.